The "smiley face method" is a visual shortcut for adding or subtracting fractions. It helps you remember the steps involved in finding a common denominator and performing the operation.
Here's how it works:
- Multiply the denominators: This gives you the common denominator. Imagine this forms the "mouth" of the smiley face.
- Cross-multiply: Multiply the numerator of the first fraction by the denominator of the second fraction. Then, multiply the numerator of the second fraction by the denominator of the first fraction. These form the "eyes" of the smiley face.
- Add or subtract the results from the cross-multiplication: Place this result as the numerator over the common denominator you found in step 1.
- Simplify: Reduce the resulting fraction to its simplest form.
Example: Adding 1/2 + 1/3
- Multiply the denominators: 2 * 3 = 6 (This is the common denominator).
- Cross-multiply:
- 1 * 3 = 3
- 1 * 2 = 2
- Add the results: 3 + 2 = 5 (This is the numerator).
- Combine: The result is 5/6.
Therefore, 1/2 + 1/3 = 5/6.
The "smiley face" visualization simply makes the cross-multiplication and common denominator process more memorable, especially for visual learners. While effective for simple fraction addition and subtraction, it's crucial to understand the underlying mathematical principles.
